Dice the chicken breast into bite-sized pieces and season with half of the salt, pepper, thyme, and rosemary.
In a medium pot, melt the ghee over medium heat and sauté the chicken until golden and cooked through, then remove and set aside.
Add the diced carrots, celery, and onion to the same pot, sautéing for 5 minutes until the vegetables begin to soften.
Pour in the chicken bone broth and the remaining herbs, bringing the mixture to a gentle simmer.
In a small bowl, whisk together the whole wheat flour, baking powder, and water until a thick dough forms.
Drop small spoonfuls of the dough into the simmering broth, covering the pot and cooking for 8-10 minutes until the dumplings are puffed.
Whisk the arrowroot powder with a splash of cold water to create a slurry, then stir it into the pot to thicken the sauce.
Add the cooked chicken back into the pot, stir gently to combine, and serve warm.